cmd/compile: move limit fact table in prove pass to dense encoding

Here begins a pretty major rewrite of the prove pass. The fundamental
observation is that although keeping facts about relations between
two SSA values could use O(n^2) space, keeping facts about relations
between an SSA value and constants needs only O(n) space. We can just
keep track of min/max for every SSA value at little cost.

Redo the limit table to just keep track of limits for all SSA values.
Use just a slice instead of a map. It may use more space (but still
just O(n) space), but accesses are a lot faster. And with the cache
in the compiler, that space will be reused quickly.

This is part of my planning to add lots more constant limits in the
prove pass.

Change-Id: Ie36819fad5631a8b79c3630fe0e819521796551a
Reviewed-on: https://go-review.googlesource.com/c/go/+/599255
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Reviewed-by: David Chase <drchase@google.com>
Reviewed-by: Michael Knyszek <mknyszek@google.com>

src/cmd/compile/internal/ssa/_gen/allocators.go

@@ -46,14 +46,14 @@ func genAllocators() {
 			maxLog:   32,
 		},
 		{
-			name:     "Int64Slice",
-			typ:      "[]int64",
+			name:     "LimitSlice",
+			typ:      "[]limit", // the limit type is basically [4]uint64.
 			capacity: "cap(%s)",
-			mak:      "make([]int64, %s)",
+			mak:      "make([]limit, %s)",
 			resize:   "%s[:%s]",
-			clear:    "for i := range %[1]s {\n%[1]s[i] = 0\n}",
-			minLog:   5,
-			maxLog:   32,
+			clear:    "for i := range %[1]s {\n%[1]s[i] = limit{}\n}",
+			minLog:   3,
+			maxLog:   30,
 		},
 		{
 			name:     "SparseSet",
@@ -92,30 +92,35 @@ func genAllocators() {
 			typ:  "[]*Block",
 			base: "ValueSlice",
 		},
+		{
+			name: "Int64",
+			typ:  "[]int64",
+			base: "LimitSlice",
+		},
 		{
 			name: "IntSlice",
 			typ:  "[]int",
-			base: "Int64Slice",
+			base: "LimitSlice",
 		},
 		{
 			name: "Int32Slice",
 			typ:  "[]int32",
-			base: "Int64Slice",
+			base: "LimitSlice",
 		},
 		{
 			name: "Int8Slice",
 			typ:  "[]int8",
-			base: "Int64Slice",
+			base: "LimitSlice",
 		},
 		{
 			name: "BoolSlice",
 			typ:  "[]bool",
-			base: "Int64Slice",
+			base: "LimitSlice",
 		},
 		{
 			name: "IDSlice",
 			typ:  "[]ID",
-			base: "Int64Slice",
+			base: "LimitSlice",
 		},
 	}
 

src/cmd/compile/internal/ssa/allocators.go

@@ -47,42 +47,42 @@ func (c *Cache) freeValueSlice(s []*Value) {
 	poolFreeValueSlice[b-5].Put(sp)
 }
 
-var poolFreeInt64Slice [27]sync.Pool
+var poolFreeLimitSlice [27]sync.Pool
 
-func (c *Cache) allocInt64Slice(n int) []int64 {
-	var s []int64
+func (c *Cache) allocLimitSlice(n int) []limit {
+	var s []limit
 	n2 := n
-	if n2 < 32 {
-		n2 = 32
+	if n2 < 8 {
+		n2 = 8
 	}
 	b := bits.Len(uint(n2 - 1))
-	v := poolFreeInt64Slice[b-5].Get()
+	v := poolFreeLimitSlice[b-3].Get()
 	if v == nil {
-		s = make([]int64, 1<<b)
+		s = make([]limit, 1<<b)
 	} else {
-		sp := v.(*[]int64)
+		sp := v.(*[]limit)
 		s = *sp
 		*sp = nil
-		c.hdrInt64Slice = append(c.hdrInt64Slice, sp)
+		c.hdrLimitSlice = append(c.hdrLimitSlice, sp)
 	}
 	s = s[:n]
 	return s
 }
-func (c *Cache) freeInt64Slice(s []int64) {
+func (c *Cache) freeLimitSlice(s []limit) {
 	for i := range s {
-		s[i] = 0
+		s[i] = limit{}
 	}
 	b := bits.Len(uint(cap(s)) - 1)
-	var sp *[]int64
-	if len(c.hdrInt64Slice) == 0 {
-		sp = new([]int64)
+	var sp *[]limit
+	if len(c.hdrLimitSlice) == 0 {
+		sp = new([]limit)
 	} else {
-		sp = c.hdrInt64Slice[len(c.hdrInt64Slice)-1]
-		c.hdrInt64Slice[len(c.hdrInt64Slice)-1] = nil
-		c.hdrInt64Slice = c.hdrInt64Slice[:len(c.hdrInt64Slice)-1]
+		sp = c.hdrLimitSlice[len(c.hdrLimitSlice)-1]
+		c.hdrLimitSlice[len(c.hdrLimitSlice)-1] = nil
+		c.hdrLimitSlice = c.hdrLimitSlice[:len(c.hdrLimitSlice)-1]
 	}
 	*sp = s
-	poolFreeInt64Slice[b-5].Put(sp)
+	poolFreeLimitSlice[b-3].Put(sp)
 }
 
 var poolFreeSparseSet [27]sync.Pool
@@ -179,14 +179,40 @@ func (c *Cache) freeBlockSlice(s []*Block) {
 	}
 	c.freeValueSlice(*(*[]*Value)(unsafe.Pointer(&b)))
 }
+func (c *Cache) allocInt64(n int) []int64 {
+	var base limit
+	var derived int64
+	if unsafe.Sizeof(base)%unsafe.Sizeof(derived) != 0 {
+		panic("bad")
+	}
+	scale := unsafe.Sizeof(base) / unsafe.Sizeof(derived)
+	b := c.allocLimitSlice(int((uintptr(n) + scale - 1) / scale))
+	s := unsafeheader.Slice{
+		Data: unsafe.Pointer(&b[0]),
+		Len:  n,
+		Cap:  cap(b) * int(scale),
+	}
+	return *(*[]int64)(unsafe.Pointer(&s))
+}
+func (c *Cache) freeInt64(s []int64) {
+	var base limit
+	var derived int64
+	scale := unsafe.Sizeof(base) / unsafe.Sizeof(derived)
+	b := unsafeheader.Slice{
+		Data: unsafe.Pointer(&s[0]),
+		Len:  int((uintptr(len(s)) + scale - 1) / scale),
+		Cap:  int((uintptr(cap(s)) + scale - 1) / scale),
+	}
+	c.freeLimitSlice(*(*[]limit)(unsafe.Pointer(&b)))
+}
 func (c *Cache) allocIntSlice(n int) []int {
-	var base int64
+	var base limit
 	var derived int
 	if unsafe.Sizeof(base)%unsafe.Sizeof(derived) != 0 {
 		panic("bad")
 	}
 	scale := unsafe.Sizeof(base) / unsafe.Sizeof(derived)
-	b := c.allocInt64Slice(int((uintptr(n) + scale - 1) / scale))
+	b := c.allocLimitSlice(int((uintptr(n) + scale - 1) / scale))
 	s := unsafeheader.Slice{
 		Data: unsafe.Pointer(&b[0]),
 		Len:  n,
@@ -195,7 +221,7 @@ func (c *Cache) allocIntSlice(n int) []int {
 	return *(*[]int)(unsafe.Pointer(&s))
 }
 func (c *Cache) freeIntSlice(s []int) {
-	var base int64
+	var base limit
 	var derived int
 	scale := unsafe.Sizeof(base) / unsafe.Sizeof(derived)
 	b := unsafeheader.Slice{
@@ -203,16 +229,16 @@ func (c *Cache) freeIntSlice(s []int) {
 		Len:  int((uintptr(len(s)) + scale - 1) / scale),
 		Cap:  int((uintptr(cap(s)) + scale - 1) / scale),
 	}
-	c.freeInt64Slice(*(*[]int64)(unsafe.Pointer(&b)))
+	c.freeLimitSlice(*(*[]limit)(unsafe.Pointer(&b)))
 }
 func (c *Cache) allocInt32Slice(n int) []int32 {
-	var base int64
+	var base limit
 	var derived int32
 	if unsafe.Sizeof(base)%unsafe.Sizeof(derived) != 0 {
 		panic("bad")
 	}
 	scale := unsafe.Sizeof(base) / unsafe.Sizeof(derived)
-	b := c.allocInt64Slice(int((uintptr(n) + scale - 1) / scale))
+	b := c.allocLimitSlice(int((uintptr(n) + scale - 1) / scale))
 	s := unsafeheader.Slice{
 		Data: unsafe.Pointer(&b[0]),
 		Len:  n,
@@ -221,7 +247,7 @@ func (c *Cache) allocInt32Slice(n int) []int32 {
 	return *(*[]int32)(unsafe.Pointer(&s))
 }
 func (c *Cache) freeInt32Slice(s []int32) {
-	var base int64
+	var base limit
 	var derived int32
 	scale := unsafe.Sizeof(base) / unsafe.Sizeof(derived)
 	b := unsafeheader.Slice{
@@ -229,16 +255,16 @@ func (c *Cache) freeInt32Slice(s []int32) {
 		Len:  int((uintptr(len(s)) + scale - 1) / scale),
 		Cap:  int((uintptr(cap(s)) + scale - 1) / scale),
 	}
-	c.freeInt64Slice(*(*[]int64)(unsafe.Pointer(&b)))
+	c.freeLimitSlice(*(*[]limit)(unsafe.Pointer(&b)))
 }
 func (c *Cache) allocInt8Slice(n int) []int8 {
-	var base int64
+	var base limit
 	var derived int8
 	if unsafe.Sizeof(base)%unsafe.Sizeof(derived) != 0 {
 		panic("bad")
 	}
 	scale := unsafe.Sizeof(base) / unsafe.Sizeof(derived)
-	b := c.allocInt64Slice(int((uintptr(n) + scale - 1) / scale))
+	b := c.allocLimitSlice(int((uintptr(n) + scale - 1) / scale))
 	s := unsafeheader.Slice{
 		Data: unsafe.Pointer(&b[0]),
 		Len:  n,
@@ -247,7 +273,7 @@ func (c *Cache) allocInt8Slice(n int) []int8 {
 	return *(*[]int8)(unsafe.Pointer(&s))
 }
 func (c *Cache) freeInt8Slice(s []int8) {
-	var base int64
+	var base limit
 	var derived int8
 	scale := unsafe.Sizeof(base) / unsafe.Sizeof(derived)
 	b := unsafeheader.Slice{
@@ -255,16 +281,16 @@ func (c *Cache) freeInt8Slice(s []int8) {
 		Len:  int((uintptr(len(s)) + scale - 1) / scale),
 		Cap:  int((uintptr(cap(s)) + scale - 1) / scale),
 	}
-	c.freeInt64Slice(*(*[]int64)(unsafe.Pointer(&b)))
+	c.freeLimitSlice(*(*[]limit)(unsafe.Pointer(&b)))
 }
 func (c *Cache) allocBoolSlice(n int) []bool {
-	var base int64
+	var base limit
 	var derived bool
 	if unsafe.Sizeof(base)%unsafe.Sizeof(derived) != 0 {
 		panic("bad")
 	}
 	scale := unsafe.Sizeof(base) / unsafe.Sizeof(derived)
-	b := c.allocInt64Slice(int((uintptr(n) + scale - 1) / scale))
+	b := c.allocLimitSlice(int((uintptr(n) + scale - 1) / scale))
 	s := unsafeheader.Slice{
 		Data: unsafe.Pointer(&b[0]),
 		Len:  n,
@@ -273,7 +299,7 @@ func (c *Cache) allocBoolSlice(n int) []bool {
 	return *(*[]bool)(unsafe.Pointer(&s))
 }
 func (c *Cache) freeBoolSlice(s []bool) {
-	var base int64
+	var base limit
 	var derived bool
 	scale := unsafe.Sizeof(base) / unsafe.Sizeof(derived)
 	b := unsafeheader.Slice{
@@ -281,16 +307,16 @@ func (c *Cache) freeBoolSlice(s []bool) {
 		Len:  int((uintptr(len(s)) + scale - 1) / scale),
 		Cap:  int((uintptr(cap(s)) + scale - 1) / scale),
 	}
-	c.freeInt64Slice(*(*[]int64)(unsafe.Pointer(&b)))
+	c.freeLimitSlice(*(*[]limit)(unsafe.Pointer(&b)))
 }
 func (c *Cache) allocIDSlice(n int) []ID {
-	var base int64
+	var base limit
 	var derived ID
 	if unsafe.Sizeof(base)%unsafe.Sizeof(derived) != 0 {
 		panic("bad")
 	}
 	scale := unsafe.Sizeof(base) / unsafe.Sizeof(derived)
-	b := c.allocInt64Slice(int((uintptr(n) + scale - 1) / scale))
+	b := c.allocLimitSlice(int((uintptr(n) + scale - 1) / scale))
 	s := unsafeheader.Slice{
 		Data: unsafe.Pointer(&b[0]),
 		Len:  n,
@@ -299,7 +325,7 @@ func (c *Cache) allocIDSlice(n int) []ID {
 	return *(*[]ID)(unsafe.Pointer(&s))
 }
 func (c *Cache) freeIDSlice(s []ID) {
-	var base int64
+	var base limit
 	var derived ID
 	scale := unsafe.Sizeof(base) / unsafe.Sizeof(derived)
 	b := unsafeheader.Slice{
@@ -307,5 +333,5 @@ func (c *Cache) freeIDSlice(s []ID) {
 		Len:  int((uintptr(len(s)) + scale - 1) / scale),
 		Cap:  int((uintptr(cap(s)) + scale - 1) / scale),
 	}
-	c.freeInt64Slice(*(*[]int64)(unsafe.Pointer(&b)))
+	c.freeLimitSlice(*(*[]limit)(unsafe.Pointer(&b)))
 }

src/cmd/compile/internal/ssa/cache.go

@@ -34,7 +34,7 @@ type Cache struct {
 	// Free "headers" for use by the allocators in allocators.go.
 	// Used to put slices in sync.Pools without allocation.
 	hdrValueSlice []*[]*Value
-	hdrInt64Slice []*[]int64
+	hdrLimitSlice []*[]limit
 }
 
 func (c *Cache) Reset() {

src/cmd/compile/internal/ssa/prove.go

@@ -173,7 +173,7 @@ type factsTable struct {
 	orderU *poset
 
 	// known lower and upper bounds on individual values.
-	limits     map[ID]limit
+	limits     []limit     // indexed by value ID
 	limitStack []limitFact // previous entries
 
 	// For each slice s, a map from s to a len(s)/cap(s) value (if any)
@@ -199,9 +199,12 @@ func newFactsTable(f *Func) *factsTable {
 	ft.orderU.SetUnsigned(true)
 	ft.facts = make(map[pair]relation)
 	ft.stack = make([]fact, 4)
-	ft.limits = make(map[ID]limit)
+	ft.limits = f.Cache.allocLimitSlice(f.NumValues())
 	ft.limitStack = make([]limitFact, 4)
 	ft.zero = f.ConstInt64(f.Config.Types.Int64, 0)
+	for i := range ft.limits {
+		ft.limits[i] = noLimit
+	}
 	return ft
 }
 
@@ -296,9 +299,8 @@ func (ft *factsTable) update(parent *Block, v, w *Value, d domain, r relation) {
 		// In fact if there is overflow/underflow, the corresponding
 		// code is unreachable because the known range is outside the range
 		// of the value's type.
-		old, ok := ft.limits[v.ID]
-		if !ok {
-			old = noLimit
+		old := ft.limits[v.ID]
+		if old == noLimit {
 			if v.isGenericIntConst() {
 				switch d {
 				case signed:
@@ -444,14 +446,14 @@ func (ft *factsTable) update(parent *Block, v, w *Value, d domain, r relation) {
 			// x-1 >= w && x > min  ⇒  x > w
 			//
 			// Useful for i > 0; s[i-1].
-			lim, ok := ft.limits[x.ID]
-			if ok && ((d == signed && lim.min > opMin[v.Op]) || (d == unsigned && lim.umin > 0)) {
+			lim := ft.limits[x.ID]
+			if lim != noLimit && ((d == signed && lim.min > opMin[v.Op]) || (d == unsigned && lim.umin > 0)) {
 				ft.update(parent, x, w, d, gt)
 			}
 		} else if x, delta := isConstDelta(w); x != nil && delta == 1 {
 			// v >= x+1 && x < max  ⇒  v > x
-			lim, ok := ft.limits[x.ID]
-			if ok && ((d == signed && lim.max < opMax[w.Op]) || (d == unsigned && lim.umax < opUMax[w.Op])) {
+			lim := ft.limits[x.ID]
+			if lim != noLimit && ((d == signed && lim.max < opMax[w.Op]) || (d == unsigned && lim.umax < opUMax[w.Op])) {
 				ft.update(parent, v, x, d, gt)
 			}
 		}
@@ -465,7 +467,7 @@ func (ft *factsTable) update(parent *Block, v, w *Value, d domain, r relation) {
 				parent.Func.Warnl(parent.Pos, "x+d %s w; x:%v %v delta:%v w:%v d:%v", r, x, parent.String(), delta, w.AuxInt, d)
 			}
 			underflow := true
-			if l, has := ft.limits[x.ID]; has && delta < 0 {
+			if l := ft.limits[x.ID]; l != noLimit && delta < 0 {
 				if (x.Type.Size() == 8 && l.min >= math.MinInt64-delta) ||
 					(x.Type.Size() == 4 && l.min >= math.MinInt32-delta) {
 					underflow = false
@@ -543,7 +545,7 @@ func (ft *factsTable) update(parent *Block, v, w *Value, d domain, r relation) {
 					// We know that either x>min OR x<=max. factsTable cannot record OR conditions,
 					// so let's see if we can already prove that one of them is false, in which case
 					// the other must be true
-					if l, has := ft.limits[x.ID]; has {
+					if l := ft.limits[x.ID]; l != noLimit {
 						if l.max <= min {
 							if r&eq == 0 || l.max < min {
 								// x>min (x>=min) is impossible, so it must be x<=max
@@ -617,13 +619,13 @@ func (ft *factsTable) isNonNegative(v *Value) bool {
 
 	// Check if the recorded limits can prove that the value is positive
 
-	if l, has := ft.limits[v.ID]; has && (l.min >= 0 || l.umax <= uint64(max)) {
+	if l := ft.limits[v.ID]; l != noLimit && (l.min >= 0 || l.umax <= uint64(max)) {
 		return true
 	}
 
 	// Check if v = x+delta, and we can use x's limits to prove that it's positive
 	if x, delta := isConstDelta(v); x != nil {
-		if l, has := ft.limits[x.ID]; has {
+		if l := ft.limits[x.ID]; l != noLimit {
 			if delta > 0 && l.min >= -delta && l.max <= max-delta {
 				return true
 			}
@@ -681,11 +683,7 @@ func (ft *factsTable) restore() {
 		if old.vid == 0 { // checkpointBound
 			break
 		}
-		if old.limit == noLimit {
-			delete(ft.limits, old.vid)
-		} else {
-			ft.limits[old.vid] = old.limit
-		}
+		ft.limits[old.vid] = old.limit
 	}
 	ft.orderS.Undo()
 	ft.orderU.Undo()
@@ -765,6 +763,7 @@ func (ft *factsTable) cleanup(f *Func) {
 		}
 		f.retPoset(po)
 	}
+	f.Cache.freeLimitSlice(ft.limits)
 }
 
 // prove removes redundant BlockIf branches that can be inferred
@@ -1261,10 +1260,7 @@ func addBranchRestrictions(ft *factsTable, b *Block, br branch) {
 			c = v
 			val -= off
 		}
-		old, ok := ft.limits[c.ID]
-		if !ok {
-			old = noLimit
-		}
+		old := ft.limits[c.ID]
 		ft.limitStack = append(ft.limitStack, limitFact{c.ID, old})
 		if val < old.min || val > old.max || uint64(val) < old.umin || uint64(val) > old.umax {
 			ft.unsat = true
@@ -1473,8 +1469,8 @@ func simplifyBlock(sdom SparseTree, ft *factsTable, b *Block) {
 			}
 			// slicemask(x + y)
 			// if x is larger than -y (y is negative), then slicemask is -1.
-			lim, ok := ft.limits[x.ID]
-			if !ok {
+			lim := ft.limits[x.ID]
+			if lim == noLimit {
 				break
 			}
 			if lim.umin > uint64(-delta) {
@@ -1493,8 +1489,8 @@ func simplifyBlock(sdom SparseTree, ft *factsTable, b *Block) {
 			// code for CtzNN if we know that the argument is non-zero.
 			// Capture that information here for use in arch-specific optimizations.
 			x := v.Args[0]
-			lim, ok := ft.limits[x.ID]
-			if !ok {
+			lim := ft.limits[x.ID]
+			if lim == noLimit {
 				break
 			}
 			if lim.umin > 0 || lim.min > 0 || lim.max < 0 {
@@ -1542,8 +1538,8 @@ func simplifyBlock(sdom SparseTree, ft *factsTable, b *Block) {
 			// Check whether, for a << b, we know that b
 			// is strictly less than the number of bits in a.
 			by := v.Args[1]
-			lim, ok := ft.limits[by.ID]
-			if !ok {
+			lim := ft.limits[by.ID]
+			if lim == noLimit {
 				break
 			}
 			bits := 8 * v.Args[0].Type.Size()
@@ -1563,11 +1559,11 @@ func simplifyBlock(sdom SparseTree, ft *factsTable, b *Block) {
 				break
 			}
 			divr := v.Args[1]
-			divrLim, divrLimok := ft.limits[divr.ID]
+			divrLim := ft.limits[divr.ID]
 			divd := v.Args[0]
-			divdLim, divdLimok := ft.limits[divd.ID]
-			if (divrLimok && (divrLim.max < -1 || divrLim.min > -1)) ||
-				(divdLimok && divdLim.min > mostNegativeDividend[v.Op]) {
+			divdLim := ft.limits[divd.ID]
+			if (divrLim != noLimit && (divrLim.max < -1 || divrLim.min > -1)) ||
+				(divdLim != noLimit && divdLim.min > mostNegativeDividend[v.Op]) {
 				// See DivisionNeedsFixUp in rewrite.go.
 				// v.AuxInt = 1 means we have proved both that the divisor is not -1
 				// and that the dividend is not the most negative integer,
@@ -1585,8 +1581,8 @@ func simplifyBlock(sdom SparseTree, ft *factsTable, b *Block) {
 			case OpConst64, OpConst32, OpConst16, OpConst8:
 				continue
 			}
-			lim, ok := ft.limits[arg.ID]
-			if !ok {
+			lim := ft.limits[arg.ID]
+			if lim == noLimit {
 				continue
 			}